A sensor system having a MEMS gyroscope. The sensor system includes a seismic mass for acquiring a measuring signal, a drive circuit, an acquisition circuit for reading out and demodulating the measuring signal, whereby a rate of rotation signal and a quadrature signal phase-shifted relative to the rate of rotation signal is generated, and a digital processing circuit for compensating an offset of the digitized rate of rotation signal using the digitized quadrature signal. The acquisition circuit and the digital processing circuit encompass a rate of rotation circuit, and a quadrature circuit for generating and processing the quadrature signal and generating a compensation signal for the offset compensation of the digitized rate of rotation signal. At least part of the quadrature circuit is operable in at least one other operating mode than the rate of rotation circuit, independently of the operating mode of the rate of rotation circuit.